Question
Find $\frac{d y}{d x}$ if, :
$
x=2 a t^2, y=a t^4
$

Answer

$
x=2 a t^2
$
Differentiating both sides w.r.t. $t$, we get
$
\begin{aligned}
& \frac{d x}{d t}=4 a t \\
& y=a t^4
\end{aligned}
$
Differentiating both sides w.r.t. t, we get
$
\begin{aligned}
& \frac{d y}{d t}=4 a t^3 \\
& \therefore \frac{d y}{d x}=\frac{\left(\frac{d y}{d t}\right)}{\left(\frac{d y}{d t}\right)}=\frac{4 a t^3}{4 a t}=t^2
\end{aligned}
$

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